I am trying to linearize two nonlinear functions which I attached. Please check the attachment there I clearly explained the formulations.
Thank you for your comments
Piecewise linearisation is the normal technique - take a look at https://www.hindawi.com/journals/mpe/2013/101376/
Your attachment seems unreadable.
Hello dear Araz,
Here's a trick that can help if you want to make the product of two variables x and y linear :
You define a new variable zxy such as :
zxy >= x+y-1
zxy
Sarah Bounejmate's trick works a little better I believe if you instead of zxy
Another possibility in case of bounded variables is to use a polytopic model, i.e., if x belongs to [a, b] and y belongs to [c, d], then the function xy is mapped to a polytope that is a linear combination whose coefficients depend on the mapped vertexes.
Dear Luis,
Truncation of the Taylor series expansion around certain point gives a linear model. This model is different from the polytope model that is also linear. The first one is a good approximation around the given point and the second one leads to linear combinations inside the polytope.
Regards,
René Galindo
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